{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:U2TTJYQBS7V4G54XKACQSZYDVD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8281751c58d48f73861675a5b38030e8d9d88f95012db5407b11752fecb4f109","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-16T16:28:57Z","title_canon_sha256":"ded18ba7f1f1ac1928db232327e130d9f2db701346d0ea52be495d4dfd79513d"},"schema_version":"1.0","source":{"id":"1310.4438","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4438","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4438v2","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4438","created_at":"2026-05-18T00:46:02Z"},{"alias_kind":"pith_short_12","alias_value":"U2TTJYQBS7V4","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"U2TTJYQBS7V4G54X","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"U2TTJYQB","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:9b88651486b3f8a961f0a3de9636729f3dccc6c8cf70434ee5f0270e524c07f1","target":"graph","created_at":"2026-05-18T00:46:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A net $(x_\\alpha)$ in a vector lattice $X$ is said to be {unbounded order convergent} (or uo-convergent, for short) to $x\\in X$ if the net $(\\abs{x_\\alpha-x}\\wedge y)$ converges to 0 in order for all $y\\in X_+$. In this paper, we study unbounded order convergence in dual spaces of Banach lattices. Let $X$ be a Banach lattice. We prove that every norm bounded uo-convergent net in $X^*$ is $w^*$-convergent iff $X$ has order continuous norm, and that every $w^*$-convergent net in $X^*$ is uo-convergent iff $X$ is atomic with order continuous norm. We also characterize among $\\sigma$-order complet","authors_text":"Niushan Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-16T16:28:57Z","title":"Unbounded order convergence in dual spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4438","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:62cfe15c393d009e530951e0107d8219f9703567985e09696169a0ba85a2080b","target":"record","created_at":"2026-05-18T00:46:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8281751c58d48f73861675a5b38030e8d9d88f95012db5407b11752fecb4f109","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-10-16T16:28:57Z","title_canon_sha256":"ded18ba7f1f1ac1928db232327e130d9f2db701346d0ea52be495d4dfd79513d"},"schema_version":"1.0","source":{"id":"1310.4438","kind":"arxiv","version":2}},"canonical_sha256":"a6a734e20197ebc377975005096703a8c41de253ec6cb67e88ac40708f4ec265","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6a734e20197ebc377975005096703a8c41de253ec6cb67e88ac40708f4ec265","first_computed_at":"2026-05-18T00:46:02.948019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:02.948019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kRXUb7TqKIO1EjPLWE2OTJZLT3AiCPAgeNVuFIyfwDLKW2c9i6rMbQ4AgWcDxUVaXy0GhxF+1kb8iU/+HzmEDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:02.948583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4438","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62cfe15c393d009e530951e0107d8219f9703567985e09696169a0ba85a2080b","sha256:9b88651486b3f8a961f0a3de9636729f3dccc6c8cf70434ee5f0270e524c07f1"],"state_sha256":"6b8f723e6d76dd97070d28c3e0757db235c13a36d50b810ff6fb77d0f8223ea2"}